Abstract
We present two path decompositions of Markov chains (with general state space) by means of harmonic functions, which are dual to each other. They can be seen as a generalization of Williams’ decomposition of a Brownian motion with drift. The results may be illustrated by a multitude of examples, but we confine ourselves to different types of random walks and the Pólya urn.
Citation
Götz Kersting. Kaya Memişoǧlu. "Path decompositions for Markov chains." Ann. Probab. 32 (2) 1370 - 1390, April 2004. https://doi.org/10.1214/009117904000000234
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